%0 Journal Article
%A Ammar, Kaouther
%A Wittbold, Petra
%A Carrillo Menéndez, José
%T Scalar conservation laws with general boundary condition and continuous flux function.
%D 2006
%@ 0022-0396
%U https://hdl.handle.net/20.500.14352/49992
%X We introduce a notion of entropy solution for a scalar conservation law on a bounded domain with nonhomogeneous boundary condition: u(t) + div Phi (u) = f on Q = (0, T) x Omega, u (0, (.))= u(0) on Q and "u = a on some part of the boundary (0, T) x partial derivative Omega." Existence and uniqueness of the entropy solution is established for any Phi is an element of C(R; R-N), u(0) is an element of L-infinity(Q), f is an element of L-infinity(Q), a is an element of L-infinity((0, T) x partial derivative Omega). In the L-1-setting, a corresponding result is proved for the more general notion of renormalised entropy solution.
%~